Class MathHelper

Contains common mathematical functions and constants.

Inheritance

Object

MathHelper

Inherited Members

Object.ToString()

Object.Equals(Object)

Object.Equals(Object, Object)

Object.ReferenceEquals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Namespace: OpenTK

Assembly: OpenTK.dll

Syntax

public static class MathHelper

Fields

E

Defines the value of E as a Single.

Declaration

public const float E = 2.71828175F

Field Value

Type	Description
Single

Log10E

Defines the base-10 logarithm of E.

Declaration

public const float Log10E = 0.4342945F

Field Value

Type	Description
Single

Log2E

Defines the base-2 logarithm of E.

Declaration

public const float Log2E = 1.442695F

Field Value

Type	Description
Single

Pi

Defines the value of Pi as a Single.

Declaration

public const float Pi = 3.14159274F

Field Value

Type	Description
Single

PiOver2

Defines the value of Pi divided by two as a Single.

Declaration

public const float PiOver2 = 1.57079637F

Field Value

Type	Description
Single

PiOver3

Defines the value of Pi divided by three as a Single.

Declaration

public const float PiOver3 = 1.04719758F

Field Value

Type	Description
Single

PiOver4

Definesthe value of Pi divided by four as a Single.

Declaration

public const float PiOver4 = 0.7853982F

Field Value

Type	Description
Single

PiOver6

Defines the value of Pi divided by six as a Single.

Declaration

public const float PiOver6 = 0.5235988F

Field Value

Type	Description
Single

ThreePiOver2

Defines the value of Pi multiplied by 3 and divided by two as a Single.

Declaration

public const float ThreePiOver2 = 4.712389F

Field Value

Type	Description
Single

TwoPi

Defines the value of Pi multiplied by two as a Single.

Declaration

public const float TwoPi = 6.28318548F

Field Value

Type	Description
Single

Methods

ApproximatelyEqual(Single, Single, Int32)

Approximates floating point equality with a maximum number of different bits. This is typically used in place of an epsilon comparison. see: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ see: https://stackoverflow.com/questions/3874627/floating-point-comparison-functions-for-c-sharp

Declaration

public static bool ApproximatelyEqual(float a, float b, int maxDeltaBits)

Parameters

Type	Name	Description
Single	a	the first value to compare
Single	b	the second value to compare
Int32	maxDeltaBits	the number of floating point bits to check

Returns

Type	Description
Boolean

ApproximatelyEqualEpsilon(Double, Double, Double)

Approximates double-precision floating point equality by an epsilon (maximum error) value. This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.

Declaration

public static bool ApproximatelyEqualEpsilon(double a, double b, double epsilon)

Parameters

Type	Name	Description
Double	a	The first float.
Double	b	The second float.
Double	epsilon	The maximum error between the two.

Returns

Type	Description
Boolean	true if the values are approximately equal within the error margin; otherwise, false.

ApproximatelyEqualEpsilon(Single, Single, Single)

Approximates single-precision floating point equality by an epsilon (maximum error) value. This method is designed as a "fits-all" solution and attempts to handle as many cases as possible.

Declaration

public static bool ApproximatelyEqualEpsilon(float a, float b, float epsilon)

Parameters

Type	Name	Description
Single	a	The first float.
Single	b	The second float.
Single	epsilon	The maximum error between the two.

Returns

Type	Description
Boolean	true if the values are approximately equal within the error margin; otherwise, false.

ApproximatelyEquivalent(Double, Double, Double)

Approximates equivalence between two double-precision floating-point numbers on a direct human scale. It is important to note that this does not approximate equality - instead, it merely checks whether or not two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is inclusive.

Declaration

public static bool ApproximatelyEquivalent(double a, double b, double tolerance)

Parameters

Type	Name	Description
Double	a	The first value to compare.
Double	b	The second value to compare·
Double	tolerance	The tolerance within which the two values would be considered equivalent.

Returns

Type	Description
Boolean	Whether or not the values can be considered equivalent within the tolerance.

ApproximatelyEquivalent(Single, Single, Single)

Approximates equivalence between two single-precision floating-point numbers on a direct human scale. It is important to note that this does not approximate equality - instead, it merely checks whether or not two numbers could be considered equivalent to each other within a certain tolerance. The tolerance is inclusive.

Declaration

public static bool ApproximatelyEquivalent(float a, float b, float tolerance)

Parameters

Type	Name	Description
Single	a	The first value to compare.
Single	b	The second value to compare·
Single	tolerance	The tolerance within which the two values would be considered equivalent.

Returns

Type	Description
Boolean	Whether or not the values can be considered equivalent within the tolerance.

BinomialCoefficient(Int32, Int32)

Calculates the binomial coefficient n above k.

Declaration

public static long BinomialCoefficient(int n, int k)

Parameters

Type	Name	Description
Int32	n	The n.
Int32	k	The k.

Returns

Type	Description
Int64	n! / (k! * (n - k)!)

Clamp(Double, Double, Double)

Clamps a number between a minimum and a maximum.

Declaration

public static double Clamp(double n, double min, double max)

Parameters

Type	Name	Description
Double	n	The number to clamp.
Double	min	The minimum allowed value.
Double	max	The maximum allowed value.

Returns

Type	Description
Double	min, if n is lower than min; max, if n is higher than max; n otherwise.

Clamp(Int32, Int32, Int32)

Clamps a number between a minimum and a maximum.

Declaration

public static int Clamp(int n, int min, int max)

Parameters

Type	Name	Description
Int32	n	The number to clamp.
Int32	min	The minimum allowed value.
Int32	max	The maximum allowed value.

Returns

Type	Description
Int32	min, if n is lower than min; max, if n is higher than max; n otherwise.

Clamp(Single, Single, Single)

Clamps a number between a minimum and a maximum.

Declaration

public static float Clamp(float n, float min, float max)

Parameters

Type	Name	Description
Single	n	The number to clamp.
Single	min	The minimum allowed value.
Single	max	The maximum allowed value.

Returns

Type	Description
Single	min, if n is lower than min; max, if n is higher than max; n otherwise.

DegreesToRadians(Double)

Convert degrees to radians

Declaration

public static double DegreesToRadians(double degrees)

Parameters

Type	Name	Description
Double	degrees	An angle in degrees

Returns

Type	Description
Double	The angle expressed in radians

DegreesToRadians(Single)

Convert degrees to radians

Declaration

public static float DegreesToRadians(float degrees)

Parameters

Type	Name	Description
Single	degrees	An angle in degrees

Returns

Type	Description
Single	The angle expressed in radians

Factorial(Int32)

Calculates the factorial of a given natural number.

Declaration

public static long Factorial(int n)

Parameters

Type	Name	Description
Int32	n	The number.

Returns

Type	Description
Int64	n!

InverseSqrtFast(Double)

Returns an approximation of the inverse square root of left number.

Declaration

public static double InverseSqrtFast(double x)

Parameters

Type	Name	Description
Double	x	A number.

Returns

Type	Description
Double	An approximation of the inverse square root of the specified number, with an upper error bound of 0.001

Remarks

This is an improved implementation of the the method known as Carmack's inverse square root which is found in the Quake III source code. This implementation comes from http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see http://www.beyond3d.com/content/articles/8/

InverseSqrtFast(Single)

Returns an approximation of the inverse square root of left number.

Declaration

public static float InverseSqrtFast(float x)

Parameters

Type	Name	Description
Single	x	A number.

Returns

Type	Description
Single	An approximation of the inverse square root of the specified number, with an upper error bound of 0.001

Remarks

This is an improved implementation of the the method known as Carmack's inverse square root which is found in the Quake III source code. This implementation comes from http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see http://www.beyond3d.com/content/articles/8/

NextPowerOfTwo(Double)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

public static double NextPowerOfTwo(double n)

Parameters

Type	Name	Description
Double	n	The specified number.

Returns

Type	Description
Double	The next power of two.

NextPowerOfTwo(Int32)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

public static int NextPowerOfTwo(int n)

Parameters

Type	Name	Description
Int32	n	The specified number.

Returns

Type	Description
Int32	The next power of two.

NextPowerOfTwo(Int64)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

public static long NextPowerOfTwo(long n)

Parameters

Type	Name	Description
Int64	n	The specified number.

Returns

Type	Description
Int64	The next power of two.

NextPowerOfTwo(Single)

Returns the next power of two that is greater than or equal to the specified number.

Declaration

public static float NextPowerOfTwo(float n)

Parameters

Type	Name	Description
Single	n	The specified number.

Returns

Type	Description
Single	The next power of two.

RadiansToDegrees(Double)

Convert radians to degrees

Declaration

public static double RadiansToDegrees(double radians)

Parameters

Type	Name	Description
Double	radians	An angle in radians

Returns

Type	Description
Double	The angle expressed in degrees

RadiansToDegrees(Single)

Convert radians to degrees

Declaration

public static float RadiansToDegrees(float radians)

Parameters

Type	Name	Description
Single	radians	An angle in radians

Returns

Type	Description
Single	The angle expressed in degrees

Swap(ref Double, ref Double)

Swaps two double values.

Declaration

public static void Swap(ref double a, ref double b)

Parameters

Type	Name	Description
Double	a	The first value.
Double	b	The second value.

Swap(ref Single, ref Single)

Swaps two float values.

Declaration

public static void Swap(ref float a, ref float b)

Parameters

Type	Name	Description
Single	a	The first value.
Single	b	The second value.